diff --git a/Makefile b/Makefile
index 1577ab7c..2367954e 100644
--- a/Makefile
+++ b/Makefile
@@ -1,11 +1,15 @@
 SHELL       := /bin/bash
 .SHELLFLAGS += -e -u -o pipefail
 
-PARALLEL_JOBS          ?= 2
 export REPOSITORY_ROOT := $(CURDIR)
 export IMAGE_NAME      ?= mailserver-testing:ci
 export NAME            ?= $(IMAGE_NAME)
 
+MAKEFLAGS              += --no-print-directory
+BATS_FLAGS             ?= --timing
+BATS_PARALLEL_JOBS     ?= 2
+BATS_FLAGS_PARALLEL    ?= $(BATS_FLAGS) --no-parallelize-within-files --jobs $(BATS_PARALLEL_JOBS)
+
 .PHONY: ALWAYS_RUN
 
 # -----------------------------------------------
@@ -33,7 +37,7 @@ backup:
 clean:
 # remove test containers and restore test/config directory
 	-@ [[ -d testconfig.bak ]] && { sudo rm -rf test/config ; mv testconfig.bak test/config ; } || :
-	-@ for CONTAINER in $$(docker ps -a --filter name='^dms-test-.*|^mail_.*|^hadolint$$|^eclint$$|^shellcheck$$' | sed 1d | cut -f 1-1 -d ' '); do docker rm -f $${CONTAINER}; done
+	-@ for CONTAINER in $$(docker ps -a --filter name='^dms-test_.*|^mail_.*|^hadolint$$|^eclint$$|^shellcheck$$' | sed 1d | cut -f 1-1 -d ' '); do docker rm -f $${CONTAINER}; done
 	-@ while read -r LINE; do [[ $${LINE} =~ test/.+ ]] && sudo rm -rf $${LINE}; done < .gitignore
 
 # -----------------------------------------------
@@ -43,19 +47,16 @@ clean:
 tests: ALWAYS_RUN
 # See https://github.com/docker-mailserver/docker-mailserver/pull/2857#issuecomment-1312724303
 # on why `generate-accounts` is run before each set (TODO/FIXME)
-	@ $(MAKE) generate-accounts tests/serial
-	@ $(MAKE) generate-accounts tests/parallel/set1
-	@ $(MAKE) generate-accounts tests/parallel/set2
-	@ $(MAKE) generate-accounts tests/parallel/set3
+	@ for DIR in tests/{serial,parallel/set{1,2,3}} ; do $(MAKE) generate-accounts "$${DIR}" ; done
 
 tests/serial: ALWAYS_RUN
-	@ shopt -s globstar ; ./test/bats/bin/bats --timing --jobs 1 test/$@/**.bats
+	@ shopt -s globstar ; ./test/bats/bin/bats $(BATS_FLAGS) test/$@/*.bats
 
 tests/parallel/set%: ALWAYS_RUN
-	@ shopt -s globstar ; ./test/bats/bin/bats --timing --jobs $(PARALLEL_JOBS) test/$@/**.bats
+	@ shopt -s globstar ; ./test/bats/bin/bats $(BATS_FLAGS_PARALLEL) test/$@/**/*.bats
 
 test/%: ALWAYS_RUN
-	@ shopt -s globstar nullglob ; ./test/bats/bin/bats --timing test/tests/**/{$*,}.bats
+	@ shopt -s globstar nullglob ; ./test/bats/bin/bats $(BATS_FLAGS) test/tests/**/{$*,}.bats
 
 # -----------------------------------------------
 # --- Lints -------------------------------------
diff --git a/docs/content/contributing/general.md b/docs/content/contributing/general.md
index 7270fcb8..d6bdcb94 100644
--- a/docs/content/contributing/general.md
+++ b/docs/content/contributing/general.md
@@ -24,11 +24,21 @@ To run the test suite, you will need to
 
     We do not support running linting, tests, etc on macOS at this time. Please use a linux VM.
 
+??? tip "Setting the Degree of Parallelization for Tests"
+
+    If your machine is capable, you can increase the amount of tests that are run simultaneously by prepending the `make clean all` command with `BATS_PARALLEL_JOBS=X` (i.e. `BATS_PARALLEL_JOBS=X make clean all`). This wil speed up the test procedure. You can also run all tests in serial by setting `BATS_PARALLEL_JOBS=1` this way.
+
+    The default value of `BATS_PARALLEL_JOBS` is 2. Increasing it to `3` requires 6 threads and 6GB of main memory; increasing it to `4` requires 8 threads and at least 8GB of main memory.
+
+!!! warning "Test Output when Running in Parallel"
+
+    When running test in parallel, BATS will run more than one test at any given time. This can result in output not being exactly what you'd expect, i.e. there could be _more_ or _less_ than you'd think. Those writing tests need to take care of this. Always test with `make clean generate-accounts tests/parallel/setX`.
+
 ??? tip "Running a Specific Test"
 
-    To run a specific test, use `make build generate-accounts test/<TEST NAME>`, where `<TEST NAME>` is the file name of the test (_for more precision use a relative path: `test/test/<PATH>`_) excluding the `.bats` suffix.
+    To run a specific test, use `make build generate-accounts test/<TEST NAME>`, where `<TEST NAME>` is the file name of the test (_for more precision use a relative path: `test/test/<PATH>`_) **excluding** the `.bats` suffix.
 
-    To run only the tests in `template.bats`, use `make test/template` (or `make test/parallel/set2/template`).
+    Example: To run only the tests in `template.bats`, use `make test/template` (or `make test/parallel/set2/template`).
 
 [Install Docker]: https://docs.docker.com/get-docker/
 
diff --git a/test/helper/common.bash b/test/helper/common.bash
index 6fc553f2..1f38b132 100644
--- a/test/helper/common.bash
+++ b/test/helper/common.bash
@@ -9,16 +9,35 @@ __load_bats_helper
 
 # -------------------------------------------------------------------
 
+# like _run_in_container_explicit but infers ${1} by using the ENV CONTAINER_NAME
 function _run_in_container() {
   run docker exec "${CONTAINER_NAME}" "${@}"
 }
 
+# @param ${1} container name [REQUIRED]
+# @param ... command to execute
+function _run_in_container_explicit() {
+  local CONTAINER_NAME=${1:?Container name must be given when using explicit}
+  shift 1
+  run docker exec "${CONTAINER_NAME}" "${@}"
+}
+
 function _default_teardown() {
   docker rm -f "${CONTAINER_NAME}"
 }
 
 # -------------------------------------------------------------------
 
+# @param ${1} program name [REQUIRED]
+# @param ${2} container name [IF UNSET: ${CONTAINER_NAME}]
+function _check_if_process_is_running() {
+  local PROGRAM_NAME=${1:?Program name must be provided explicitly}
+  local CONTAINER_NAME=${2:-${CONTAINER_NAME}}
+  _run_in_container_explicit "${CONTAINER_NAME}" pgrep "${PROGRAM_NAME}"
+}
+
+# -------------------------------------------------------------------
+
 # @param ${1} timeout
 # @param --fatal-test <command eval string> additional test whose failure aborts immediately
 # @param ... test to run
diff --git a/test/helper/setup.bash b/test/helper/setup.bash
index 522cfc84..4bab5925 100644
--- a/test/helper/setup.bash
+++ b/test/helper/setup.bash
@@ -17,14 +17,15 @@ function __initialize_variables() {
     'CONTAINER_NAME'
   )
 
-  for VARIABLE in "${REQUIRED_VARIABLES_FOR_TESTS}"
+  for VARIABLE in "${REQUIRED_VARIABLES_FOR_TESTS[@]}"
   do
     __check_if_set "${VARIABLE}"
   done
 
+  export SETUP_FILE_MARKER TEST_TIMEOUT_IN_SECONDS NUMBER_OF_LOG_LINES
+  SETUP_FILE_MARKER="${BATS_TMPDIR:?}/$(basename "${BATS_TEST_FILENAME:?}").setup_file"
   TEST_TIMEOUT_IN_SECONDS=${TEST_TIMEOUT_IN_SECONDS:-120}
   NUMBER_OF_LOG_LINES=${NUMBER_OF_LOG_LINES:-10}
-  SETUP_FILE_MARKER="${BATS_TMPDIR:?}/$(basename "${BATS_TEST_FILENAME:?}").setup_file"
 }
 
 # -------------------------------------------------------------------
@@ -118,6 +119,8 @@ function common_container_create() {
     --env ENABLE_UPDATE_CHECK=0 \
     --env ENABLE_SPAMASSASSIN=0 \
     --env ENABLE_FAIL2BAN=0 \
+    --env POSTFIX_INET_PROTOCOLS=ipv4 \
+    --env DOVECOT_INET_PROTOCOLS=ipv4 \
     --env LOG_LEVEL=debug \
     "${X_EXTRA_ARGS[@]}" \
     "${IMAGE_NAME}"
diff --git a/test/helper/tls.bash b/test/helper/tls.bash
index 4987a66f..bb107a4f 100644
--- a/test/helper/tls.bash
+++ b/test/helper/tls.bash
@@ -1,21 +1,17 @@
 #!/bin/bash
 
-load "${REPOSITORY_ROOT}/test/test_helper/common"
+load "${REPOSITORY_ROOT}/test/helper/common"
 
-# Helper methods for testing TLS.
 # `_should_*` methods are useful for common high-level functionality.
 
-
 # ? --------------------------------------------- Negotiate TLS
 
-
 # For certs actually provisioned from LetsEncrypt the Root CA cert should not need to be provided,
 # as it would already be available by default in `/etc/ssl/certs`, requiring only the cert chain (fullchain.pem).
 function _should_succesfully_negotiate_tls() {
   local FQDN=${1}
-  local CONTAINER_NAME=${2:-${TEST_NAME}}
   # shellcheck disable=SC2031
-  local CA_CERT=${3:-${TEST_CA_CERT}}
+  local CA_CERT=${2:-${TEST_CA_CERT}}
 
   # Postfix and Dovecot are ready:
   wait_for_smtp_port_in_container_to_respond "${CONTAINER_NAME}"
@@ -36,9 +32,8 @@ function _should_succesfully_negotiate_tls() {
 function _negotiate_tls() {
   local FQDN=${1}
   local PORT=${2}
-  local CONTAINER_NAME=${3:-${TEST_NAME}}
   # shellcheck disable=SC2031
-  local CA_CERT=${4:-${TEST_CA_CERT}}
+  local CA_CERT=${3:-${TEST_CA_CERT}}
 
   local CMD_OPENSSL_VERIFY
   CMD_OPENSSL_VERIFY=$(_generate_openssl_cmd "${PORT}")
@@ -83,7 +78,6 @@ function _generate_openssl_cmd() {
   echo "${CMD_OPENSSL} ${EXTRA_ARGS} 2>/dev/null"
 }
 
-
 # ? --------------------------------------------- Verify FQDN
 
 function _get_fqdn_match_query() {
@@ -115,9 +109,8 @@ function escape_fqdn() {
 function _get_fqdns_for_cert() {
   local FQDN=${1}
   local PORT=${2:-'25'}
-  local CONTAINER_NAME=${3:-${TEST_NAME}}
   # shellcheck disable=SC2031
-  local CA_CERT=${4:-${TEST_CA_CERT}}
+  local CA_CERT=${3:-${TEST_CA_CERT}}
 
   # `-servername` is for SNI, where the port may be for a service that serves multiple certs,
   # and needs a specific FQDN to return the correct cert. Such as a reverse-proxy.